| d1 | d2 | Straight | Advantage | Disadvantage |
|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 |
| 1 | 2 | 1 | 2 | 1 |
| 1 | 3 | 1 | 3 | 1 |
| 1 | 4 | 1 | 4 | 1 |
| 1 | 5 | 1 | 5 | 1 |
| 1 | 6 | 1 | 6 | 1 |
| 1 | 7 | 1 | 7 | 1 |
An Analysis of Advantage/Disadvantage in the D20 System
Who Am I?
Explain D&D and the d20 System
Test Intuition
Simulate Mechanisms
Illustrate Typical Examples
Uncertain outcomes resolved with dice
Polyhedral dice
Mostly use d20 (20-sided die)
Used for direct contests
Introduced in Fifth Edition (5e)
Roll 2d20
Keep Highest (Advantage)
Keep Lowest (Disadvantage)
Discrete space
No need for simulation
\[\begin{eqnarray*} 1\text{d}20 &\rightarrow& 20 \text{ possible outcomes} \\ 2\text{d}20 &\rightarrow& 400 \text{ possible outcomes} \end{eqnarray*}\]
Create table of outcomes for 2d20.
\[\begin{eqnarray*} \text{Straight: } &\rightarrow& \text{ use first die} \\ \text{Adv/Disadv: } &\rightarrow& \text{ use max/min of two dice} \\ \text{ROLL(P/M)#: } &\rightarrow& \text{ adjust first die} \end{eqnarray*}\]
| d1 | d2 | Straight | Advantage | Disadvantage |
|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 |
| 1 | 2 | 1 | 2 | 1 |
| 1 | 3 | 1 | 3 | 1 |
| 1 | 4 | 1 | 4 | 1 |
| 1 | 5 | 1 | 5 | 1 |
| 1 | 6 | 1 | 6 | 1 |
| 1 | 7 | 1 | 7 | 1 |
Subclass of Fighter
Critical Hit on 19 or 20
What is the impact of advantage / disadvantage
| Roll Type | Target | Success Prob | Failure Prob |
|---|---|---|---|
| Straight | 19 | 0.1000 | 0.9000 |
| Straight | 20 | 0.0500 | 0.9500 |
| Advantage | 19 | 0.1900 | 0.8100 |
| Advantage | 20 | 0.0975 | 0.9025 |
| Disadvantage | 19 | 0.0100 | 0.9900 |
| Disadvantage | 20 | 0.0025 | 0.9975 |
Resolve Contests
Both Roll 1d20, add bonus
Discrete Space
Bigger and messier
Use simulation
16 STR / Prof (+5 to roll) -> AC 13
Needs 8 or higher on attack roll
| Roll Type | Success | Failure | Failure Ratio |
|---|---|---|---|
| Straight | 0.6500 | 0.3500 | 1.00 |
| Advantage | 0.8775 | 0.1225 | 0.35 |
| Disadvantage | 0.4225 | 0.5775 | 1.65 |
18 STR / Prof (+7 to roll) -> AC 10
Needs 3 or higher on attack roll
| Roll Type | Success | Failure | Failure Ratio |
|---|---|---|---|
| Straight | 0.90 | 0.10 | 1.0 |
| Advantage | 0.99 | 0.01 | 0.1 |
| Disadvantage | 0.81 | 0.19 | 1.9 |
10 STR / Not proficient (+0 to roll) -> AC 18
Needs 18 or higher on attack roll
| Roll Type | Success | Failure | Failure Ratio |
|---|---|---|---|
| Straight | 0.1500 | 0.8500 | 1.00 |
| Advantage | 0.2775 | 0.7225 | 0.85 |
| Disadvantage | 0.0225 | 0.9775 | 1.15 |
Pavluk of Pelor
Fighting Large Wolf
20% -> AC 13
80% -> AC 14
20% -> +5 attack, 1d12 + 3
70% -> +6 attack, 1d12 + 4
10% -> +7 attack, 1d12 + 5
Move and Help the Rogue
Cast Guiding Bolt
Move and Help the Champion
Move beside Rogue
Help action (+5 attack, +1d6)
Give advantage
Cast Guiding Bolt
+5 attack, 4d6 damage, grants advantage
Move beside Wolf
Help Champion (+6 attack, 2d6 damage)
Give advantage
| Option | Miss Prop | Mean | Median | P10 | P90 |
|---|---|---|---|---|---|
| Help Rogue | 0.0681 | 19.30 | 19 | 9 | 30 |
| Cast Spell | 0.0813 | 25.87 | 26 | 8 | 44 |
| Help Champion | 0.0727 | 13.61 | 14 | 6 | 22 |
Looks like Pavluk is spell-casting…
+/- 3 on average (all test difficulties)
Advantage about +4 for gameplay
Non-linearity
Effects non-intuitive
Stand-Up Maths YouTube Channel
https://www.youtube.com/watch?v=X_DdGRjtwAo
Joseph Newton
This talk…
https://github.com/kaybenleroll/data_workshops/talk_gaming_dndadv_202301